In [1]:
# prepared by Sam. feel free to consult (sirmaxford@gmail.com).
import matplotlib.pyplot as plt; import pandas as pd; import numpy as np
from scipy.optimize import curve_fit
from scipy.interpolate import interp1d
from scipy.signal import savgol_filter
from scipy.interpolate import UnivariateSpline
%matplotlib inline
font = {'family': 'serif',
        'color':  'darkred',
        'weight': 'normal',
        'size': 14,
        }
In [2]:
columns = ['r', 'b', 'atp', 'md', 'v_av', 'v_sd']
df = pd.read_csv('vel_changes.csv', names=columns)
In [3]:
df[0:10]
Out[3]:
r b atp md v_av v_sd
0 0.1 13 2000 3000 0.09893 0.08043
1 0.2 13 2000 3000 0.49694 0.44099
2 0.3 13 2000 3000 5.14376 3.07438
3 0.4 13 2000 3000 5.41553 2.34461
4 0.5 13 2000 3000 6.04005 3.28116
5 0.6 13 2000 3000 6.66972 1.15667
6 0.7 13 2000 3000 6.79622 1.10787
7 0.8 13 2000 3000 6.76524 1.07794
8 0.9 13 2000 3000 6.56418 1.04057
9 1.0 13 2000 3000 6.39632 0.53641
In [4]:
r_change = df[0:10]
In [5]:
r_change['v_av']
Out[5]:
0    0.09893
1    0.49694
2    5.14376
3    5.41553
4    6.04005
5    6.66972
6    6.79622
7    6.76524
8    6.56418
9    6.39632
Name: v_av, dtype: float64
In [6]:
x = r_change['r']
y = r_change['v_av']
xx = np.linspace(x.min(), x.max(), 1000)

# interpolate + smooth
itp = interp1d(x,y, kind='linear')
window_size, poly_order = 101, 3
yy_sg = savgol_filter(itp(xx), window_size, poly_order)

# or fit to a global function
def func(x, A, B, x0, sigma):
    return A+B*np.tanh((x-x0)/sigma)

fit, _ = curve_fit(func, x, y) #, bounds=(0.0,[1.0,0.3,0.6]))
yy_fit = func(xx, *fit)

#s = UnivariateSpline(x, y, s=2)
#xs = np.linspace(x.min(), x.max(), 100)
#ys = s(xs)

/home/nitta/.local/lib/python3.5/site-packages/scipy/signal/_arraytools.py:45: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.
  b = a[a_slice]
/home/nitta/.local/lib/python3.5/site-packages/pandas/core/computation/check.py:17: UserWarning: The installed version of numexpr 2.4.3 is not supported in pandas and will be not be used
The minimum supported version is 2.4.6

  ver=ver, min_ver=_MIN_NUMEXPR_VERSION), UserWarning)

$f(x) = A + B \tanh\left(\frac{x-x_0}{\sigma}\right)$

In [7]:
#plt.figure(figsize=(10,8))
plt.figure(figsize=(14,10), dpi=500)
#plt.plot(xx, yy_sg, 'k', label= "Smoothed curve")
#plt.plot(xs, ys)
plt.plot(xx, yy_fit, 'c--', linewidth=3.5, label= "Curve fit")
plt.errorbar(x,y,yerr=r_change['v_sd'], ecolor='b', capsize=7, \
             mec='blue', color='green', marker='D', linewidth=2, \
             markersize=7, label='Mean Velocity Deviation: ATP = 2000, MD = 3000')
plt.xlabel('Specie Ratio', fontdict=font); plt.ylabel('Mean Velocity', fontdict=font)
plt.title('Actin Filament Movement'); plt.legend(loc='upper left'); plt.grid()
In [8]:
df[10:25]
Out[8]:
r b atp md v_av v_sd
10 0.9 13 300 3000 3.16475 0.42185
11 0.9 13 600 3000 4.48637 0.46199
12 0.9 13 900 3000 5.22617 0.92963
13 0.9 13 1200 3000 5.47609 0.44497
14 0.9 13 1500 3000 6.15356 0.56837
15 0.9 13 1800 3000 6.38277 1.16754
16 0.9 13 2100 3000 6.64491 0.93268
17 0.9 13 2400 3000 6.67938 0.61918
18 0.9 13 2700 3000 6.65730 0.78833
19 0.9 13 3000 3000 7.02342 0.40345
20 0.9 13 3300 3000 7.15628 1.10814
21 0.9 13 3600 3000 7.31357 1.08375
22 0.9 13 3900 3000 7.16177 0.61391
23 0.9 13 4200 3000 7.29127 0.83575
24 0.9 13 4500 3000 7.34592 0.92825
In [9]:
atp_change = df[10:25]
In [10]:
x = atp_change['atp']
y = atp_change['v_av']
xx = np.linspace(x.min(), x.max(), 1000)

# interpolate + smooth
itp = interp1d(x,y, kind='linear')
window_size, poly_order = 101, 3
yy_sg = savgol_filter(itp(xx), window_size, poly_order)

# or fit to a global function
#def func(x, A, B, x0, sigma):
#    return A+B*np.tanh((x-x0)/sigma)

def func(x, a, b, c):
    return a * np.exp(-b * x) + c

fit, _ = curve_fit(func, x, y)
yy_fit = func(xx, *fit)

/home/nitta/.local/lib/python3.5/site-packages/scipy/signal/_arraytools.py:45: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.
  b = a[a_slice]
/home/nitta/.local/lib/python3.5/site-packages/scipy/optimize/minpack.py:794: OptimizeWarning: Covariance of the parameters could not be estimated
  category=OptimizeWarning)
In [11]:
plt.figure(figsize=(14,10), dpi=500)
#plt.plot(xx, yy_fit, 'c--', linewidth=3.5, label= "Curve fit")
plt.errorbar(x,y,yerr=atp_change['v_sd'], ecolor='b', capsize=7, \
             mec='blue', color='green', marker='D', linestyle='-', linewidth=2, \
             markersize=7, label='Mean Velocity Deviation: Ratio = 90%, MD = 3000')
plt.xlabel('ATP', fontdict=font); plt.ylabel('Mean Velocity', fontdict=font)
plt.title('Actin Filament Movement'); plt.legend(loc='upper left'); plt.grid()
In [12]:
df[25:30]
Out[12]:
r b atp md v_av v_sd
25 0.9 13 2000 1000 5.93888 2.88525
26 0.9 13 2000 2000 6.73108 1.30774
27 0.9 13 2000 3000 6.56418 1.04057
28 0.9 13 2000 4000 6.39449 0.50562
29 0.9 13 2000 5000 5.77560 1.90921
In [13]:
md_change = df[25:30]
In [14]:
plt.figure(figsize=(14,10), dpi=500)
plt.errorbar(md_change['md'],md_change['v_av'],yerr=md_change['v_sd'], ecolor='b', capsize=7, \
             mec='blue', color='green', marker='D', linestyle='-', linewidth=2, \
             markersize=7, label='Mean Velocity Deviation: Ratio = 90%, ATP = 2000')
plt.xlabel('Motor Density', fontdict=font); plt.ylabel('Mean Velocity', fontdict=font)
plt.title('Actin Filament Movement'); plt.legend(loc='upper left'); plt.grid()
In [15]:
conf_names = ['beads', 'x', 'y', 'z']
df_conf = pd.read_csv('Conformation_A001.txt', names=conf_names, delim_whitespace=True)
df_conf_good = pd.read_csv('Conformation_A001_good.txt', names=conf_names, delim_whitespace=True)
df_conf = df_conf.drop(['beads', 'x', 'y'], axis=1)
df_conf_good = df_conf_good.drop(['beads', 'x', 'y'], axis=1)
df_conf = df_conf[13:]
df_conf_good = df_conf_good[13:]
df_z = df_conf.iloc[0::13, :]
df_z_good = df_conf_good.iloc[0::13, :]
In [16]:
df_z.shape
Out[16]:
(300, 1)
In [17]:
tip_names = ['time', 'x_tip', 'y_tip']
df_tip = pd.read_csv('TipXY_A001.txt', names=tip_names, delim_whitespace=True)
df_tip_good = pd.read_csv('TipXY_A001_good.txt', names=tip_names, delim_whitespace=True)
df_time = df_tip.drop(columns=['x_tip','y_tip'])
df_time_good = df_tip.drop(columns=['x_tip','y_tip'])
df_time = df_time[1:]
df_time_good = df_time[0:]
df_time_good.shape
Out[17]:
(300, 1)
In [18]:
Dx_tip = np.diff(df_tip['x_tip']); Dy_tip = np.diff(df_tip['y_tip'])
Dx_tip_good = np.diff(df_tip_good['x_tip']); Dy_tip_good = np.diff(df_tip_good['y_tip'])
dist=np.sqrt((Dx_tip**2)+(Dy_tip**2))
dist_good=np.sqrt((Dx_tip_good**2)+(Dy_tip_good**2))
tym=0.01
vel_tip = dist/tym
vel_tip_good = dist_good/tym
df_vel_tip = pd.DataFrame(data=vel_tip)
df_vel_tip_good = pd.DataFrame(data=vel_tip_good)
df_vel_tip.shape
Out[18]:
(300, 1)

R1.0B3ATP3000MD4000

R1.0B13.0ATP3000.0MD4000.0

R1.0B3ATP3000MD4000

In [19]:
fig, ax1 = plt.subplots(dpi=500)
ax1.plot(df_time_good,df_z_good, 'b', label='Actin Z-Variations')
ax1.set_xlabel('Time (s)',fontdict=font)
ax1.set_ylabel('Z-Distance', color='b',fontdict=font)
ax1.tick_params('y', colors='b')
plt.legend(loc='upper left')

ax2 = ax1.twinx()
ax2.plot(df_time_good,df_vel_tip_good, 'r', label='Tip Velocity')
fig.set_size_inches([15, 7])
fig.tight_layout()
ax2.set_ylabel('Tip-Velocity', color='r',fontdict=font)
ax2.tick_params('y', colors='r')
plt.title('Actin Filament Movement',fontdict=font); plt.legend(loc='upper right')
plt.grid(); plt.show()

R1.0B3ATP3000MD4000

In [20]:
#df_z_good.to_csv('df_z_good', encoding='utf-8', index=False)
#df_vel_tip_good.to_csv('df_vel_tip_good', encoding='utf-8', index=False)
In [21]:
c_names = ['Change in Z', 'Tip Velocity']
z_and_tip_vel_good = pd.read_csv('z_and_tip_vel_good.csv', names=c_names)
z_and_tip_vel_good.corr()
Out[21]:
Change in Z Tip Velocity
Change in Z 1.000000 0.086935
Tip Velocity 0.086935 1.000000
In [22]:
fig = plt.figure(figsize=(14,10), dpi=500)
ax = fig.gca()
df_z_good.hist(bins=100, ax=ax, color='green')
Out[22]:
array([<matplotlib.axes._subplots.AxesSubplot object at 0x7f753048f748>],
      dtype=object)

R1.0B3ATP3000MD4000

R0.9LAF3ATP3300MD3000

R0.9LAF3ATP3300MD3000

In [23]:
fig, ax1 = plt.subplots(dpi=500)
ax1.plot(df_time,df_z, 'b', label='Actin Z-Variations')
ax1.set_xlabel('Time (s)',fontdict=font)
ax1.set_ylabel('Z-Distance', color='b',fontdict=font)
ax1.tick_params('y', colors='b')
plt.legend(loc='upper left')

ax2 = ax1.twinx()
ax2.plot(df_time,df_vel_tip, 'r', label='Tip Velocity')
fig.set_size_inches([15, 7])
fig.tight_layout()
ax2.set_ylabel('Tip-Velocity', color='r',fontdict=font)
ax2.tick_params('y', colors='r')
plt.title('Actin Filament Movement',fontdict=font); plt.legend(loc='upper right')
plt.grid(); plt.show()

R0.9LAF3ATP3300MD3000

In [24]:
#df_z.columns = ['Change in Z']
#df_vel_tip.columns = ['Tip Velocity']
#df_z = df_z.reset_index(drop=True)
#df_z.merge(df_vel_tip, how='left', left_on='Change in Z', right_on='Tip Velocity')
#np.array(df_z, df_vel_tip)

#df_z.to_csv('df_z', encoding='utf-8', index=False)
#df_vel_tip.to_csv('df_vel_tip', encoding='utf-8', index=False)
In [25]:
c_names = ['Change in Z', 'Tip Velocity']
z_and_tip_vel = pd.read_csv('z_and_tip_vel.csv', names=c_names)
z_and_tip_vel.corr()
Out[25]:
Change in Z Tip Velocity
Change in Z 1.00000 0.13868
Tip Velocity 0.13868 1.00000
In [26]:
fig = plt.figure(figsize=(14,10), dpi=500)
ax = fig.gca()
df_z.hist(bins=100, ax=ax, color='green')
Out[26]:
array([<matplotlib.axes._subplots.AxesSubplot object at 0x7f75303ab828>],
      dtype=object)

R0.9LAF3ATP3300MD3000

In [ ]: